Deep active learning for constitutive modelling of granular materials: From representative volume elements to implicit finite element modelling

Abstract

Constitutive relation remains one of the most important, yet fundamental challenges in the study of granular materials. Instead of using closed-form phenomenological models or numerical multiscale modelling, machine learning has emerged as an alternative paradigm to revolutionise the constitutive modelling of granular materials. However, deep neural networks (DNNs) require massive training data and often fail to make credible extrapolations. This study aims to develop a deep active learning strategy to (i) identify unreliable forecasts without knowing the ground truth; and (ii) continuously improve and verify a data-driven constitutive model until the desired generalisation is satisfied. The role of active learning in constitutive modelling is instantiated through three scenarios: (i) off-line strain-stress data pool of granular materials; (ii) interactive constitutive training and strain-stress data labelling; and (iii) finite element modelling (FEM) driven by deep learning-based constitutive models. The results confirm the capability of active learning in advancing data-driven constitutive modelling of granular materials toward developing a faithful surrogate constitutive model with less data. The same active learning strategy can also be applied to other data-centric applications across various science and engineering fields.